Question

Jamal is hanging up Christmas lights in his front yard to mimic the look of a Christmas tree. He starts by placing a pole in the ground and then extending strands of lights from the top of the pole to the ground in a circular pattern. The pole is 9 feet tall once placed in the ground, and each light strand is 16 feet long. If he attaches a strand of lights to the top of the pole and extends it down to the ground, what is the angle formed between the light strand and the pole? Round your answer to the nearest tenth.

Answer 1

Make a right triangle with the pole as the vertical leg (9 ft) and the strand as the hypotenuse (16 ft). If θ is the angle between pole and strand, then

cos θ = adjacent/hypotenuse = 9/16.

So θ = arccos(9/16) ≈ 55.9° (to the nearest tenth).